Point averaging of the position components, before and after S/A is turned off

Abstract
A Low Cost GPS engine was used in this research. First of all a suitable hardware was designed and used to collect and save the receiver’s output data, with S/A on, by a special software. This was also repeated with S/A off. Another software was also written to draw variations in position measurement errors in two different conditions mentioned above. Finally, a simple post processing technique, point averaging was used, and the data were averaged in various periods of time for S/A on and off. The decrease in measurement errors was proportionate to the duration of averaging.

Introduction
During past several years, the main problem in improving of the positioning measuring accuracy was Selective Availability (S/A) error. Which was produced and fed into GPS system by U.S. Department of Defense (DoD) in order to degrade the achievable navigation accuracy when non-military GPS receivers are used. In addition to S/A, there is some other error sources that cause the position and time measuring from GPS receivers to be inaccurate [1,2].

**Table 1: Average error introduced per satellites**
Error Source	Error (meters)	Time Constant
Receiver Noise	0.4	-
Troposphere	0.5	>1 hour
Signal Multi path	0.6	0.5 to 10 min
Satellite clocks	1.5	-
Orbit Errors	2.5	>1 hour
Ionosphere	5.0	> 1 hour
Selective Availability	30	» 2 min.

Other significant error sources are signal delays from ionospheric and tropospheric effects, satellite clock drift, satellite orbital position errors, signal multi path, and noise generated within the receiver itself. Table 1 shows the average error introduced per satellite in GPS systems [3].

Because of above mentioned error sources, all GPS collected points have a certain number of errors. This means that the location we grant will not reflect the real location. Therefore, users who wish to increase the accuracy of their GPS receiver must take steps to minimize the errors. Post processing techniques offers GPS users an affordable and relatively easy mean for correcting GPS errors.

The simplest post processing technique is Point Averaging, which relies on simple arithmetic to correct GPS errors. So, if we collected many points and then averaged them together, we could feel confident that the majority of points were fairly close to the real location and the effects of all outliners would be minimal [4,5].

GPS Receiver
There are a wide variety of GPS receiver products in today’s market. Some are complete systems containing keyboards and LCD displays such as hand held receivers, and some are available as electronic boards, called Original Equipment Manufacturer (OEM) products.

We used the Rockwell “ Microtracker LP (MLP)” receiver, which is a low cost single board, single frequency, C/A code, five parallel-channel, GPS engine suitable for integration into a wide variety OEM products.

Two serial data ports are provided with the MLP. One is used to output position components, velocity, time Information, and status information to the OEM’s application software input initialization data, and commands are received over the same serial data port. A second serial port is dedicated to DGPS1 correction input. Since the output data of the receiver are available in NMEA2 and Binary protocols, and the Binary protocol provides more detailed information, the receiver was initialized to communicate Binary protocols. There are several Binary messages provided by MLP. One famous and general purpose of these messages is message No. 103, which is available on the first output port as default, when we configure the receiver in Binary mode. We designed and implemented a hardware in order to setup the receiver and connect it to a PC. Figure 1 shows the hardware structure [6,7].

Data Collection
We developed a software to collect and save the raw data received from GPS receiver. Then we set the receiver in a known position and saved the long-term raw data collected from Binary Message No.103. Once we execute this program, the system asks for a binary filename in order to saving the data. Then it starts to collect and save the received data in the binary file. Data collecting has been in two different periods, before and after 1st May 2000 (June to December 1999, and July to September 2001).

Table 2: Error reduction by point averaging. (S/A on)
Time of Averaging	X Component		Y Component		Z Component
Time of Averaging	Standard Deviation	Amplitude	Standard Deviation	Amplitude	Standard Deviation	Amplitude
Raw data	43.2	345	45.5	360	48	393
5 min	26.5	75.6	30.2	82.2	27.6	92.8
10 min	19.3	50.5	26	77.8	20.4	68
45 min	15.8	49.6	9.6	25.3	5.4	17.2
1 hour	12.2	32.9	5.9	18.2	4.6	12.7
5 hour	4.9	14.2	5.4	17.9	4	11.5

Later, we sketched the variation in position components (X, Y, and Z in WGS 84 system) due to time, by a software developed for this purpose. Figure 2 and 3 show these variations, before and after S/A is turned off respectively. As the graphs show, the errors have clearly been reduced after turning S/A off. Measurements for 6 months data collecting in two periods, show that maximum of error amplitude in presence of S/A is more Than 300 meters while without S/A this quantity reduces to tens of meters.

Finally, wards, we averaged position components for various periods of time (5, 10, 45, 60 minutes & 5 hours) using a recursivealgorithm based on the following equations:

X_n+1 = ((n-1)/n) X_n + (1/n) X_n+1 (1)
Y_n+1 = ((n-1)/n) Y_n + (1/n) Y_n+1 (2)
Z_n+1 = ((n-1)/n) Z_n + (1/n) Z_n+1 (3)

Where X, Y and Z are measured position components, and n is the number of measurements.

The results of averaging for data collected while S/A was on are shown in table 3. Those for the period in which S/A was off are given in table 4.

Table 3: Error reduction by point averaging. (S/A off)
Time of Averaging	X Component		Y Component		Z Component
Time of Averaging	Standard Deviation	Amplitude	Standard Deviation	Amplitude	Standard Deviation	Amplitude
Raw data	8.3	39	7.9	34.5	9.2	43.6
5 min	7.1	31.5	6.7	28.8	7.5	33
10 min	5.2	24	4.5	22.7	5.3	25.6
45 min	3.2	13.1	3	12.5	2.9	11.1
1 hour	2.2	7.7	2.3	8.2	2.3	9.1
5 hour	2.1	7.4	2.2	7.6	2.3	7.9

Conclusion
In this research, we studied and saved position parameters received from a Low Cost GPS engine both in presence and absence of intentional errors (S/A). This measurement was performed for a known position. The results show that the measured position components are more accurate in the absence of S/A than its presence. Averaging the raw position components improved the accuracy of our measurement, which was increased, with the duration of averaging. So, that position measurement error before turning off the S/A, was decreased from more than 300 to less than 18 meters after averaging. Similarly, the error was reduced to less than 8 meters after turning off the S/A, while it was about 40 meter before averaging.

References

Hofmann-Wellenhof, H. Lichtenegger, J. Collins, Global Positioning Systerm Theory and Practice, Third revised edition, ISBN 3-211-82591-6, Springer-Verlag Wien New York April 1994.
Timothy Barnes, Selective Availability via the Levinson Predictor, ION GPS-95, September 1995, P.P. 533-542.
GPS Error Sources, Axiom Navigation Incorporated, www.axiomnav.com/differential-gps, 2001.
Point Averaging, University of North Carolina, www.cpc.unc.edu/services/spatial/postproc.htm, 27 January, 2000.
Ian Strachan, 2000, GPS System Accuracy After 1 May 2000, Some UK Test Without DGPS and SA off, 4 May 2000, http://joe.mehaffey.com/saoffaccuracy.htm
Microtracker LP Designer’s Guide, Rockwell International Corporation, GPS-22, January 1, 1995.
Microtracker LP Operations Manual, Rockwell International Corporation, GPS-16, January 10, 1994.